English

On a supercongruence conjecture of Rodriguez-Villegas

Number Theory 2012-04-10 v1

Abstract

In examining the relationship between the number of points over Fp\mathbb{F}_p on certain Calabi-Yau manifolds and hypergeometric series which correspond to a particular period of the manifold, Rodriguez-Villegas identified numerically 22 possible supercongruences. We prove one of the outstanding supercongruence conjectures between a special value of a truncated generalized hypergeometric series and the pp-th Fourier coefficient of a modular form.

Keywords

Cite

@article{arxiv.1204.1575,
  title  = {On a supercongruence conjecture of Rodriguez-Villegas},
  author = {Dermot McCarthy},
  journal= {arXiv preprint arXiv:1204.1575},
  year   = {2012}
}